5 not in r4c1, it is in r6c1 or r6c2 (Row on 3x3 Block interaction)
1 not in r8c6, it is in r7c4 or r7c6 (same)
9 not in r4c8, XY-Wing-2 X=6 Y=1 in r5c3 X=6 Z=9 in r5c8 Y=1 Z=9 in r4c1
9 in r4c1 9 in r5c8 - Unique Horizontal
...

IF I KNEW WHAT AN XY-WING WAS I WOULD TRY TO FIND IT. COULD YOU LET ME KNOW WHAT ONE IS? IN SIMPLE TERMS PLEASE.
I NEVER HAD A 5 IN R4 C1 - I HAD JUST A 1 AND A 9 - THE RET OF WHAT YOU SAY I DO HAVE. THANKS FOR THE HELP. H

Here, Holly -- I'll help you understand the "xy-wing." Or at least, I will try.

At the point you've reached in the puzzle, there are four critical cells. These are r4c1, r4c8, r5c3, and r5c8. If you analyze these cells carefully you will see that only the following values are possible at these four locations.

r4c1 is either 1 or 9.
r4c8 is either 5, 6, or 9.
r5c3 is either 1 or 6.
r5c8 is either 6 or 9.

Consider what would happen if one were to place a "1" at r5c3. Then r4c1 would be a "9" (in the same 3x3 box) and "9" would be ruled out at r4c8.

What if there's a "6" at r5c3? Then r5c8 would be a "9", and "9" would still be ruled out at r4c8.

Either way, then, there cannot be a "9" at r4c8 -- the only place where a "9" can fit in row 4 is therefore r4c1, and the puzzle can be easily solved from there.

There has been a lot of discussion of the "xy-wing" in the "Other puzzles" section of this forum -- try reading about it here or here or here or here. dcb

I'm probably the wrong guy to ask, Holly. I still have difficulty locating these.

The "XY-Wing" always involves four cells in the puzzle, and three of these must contain values that fit the general pattern {X, Y}, {X, Z}, {Y, Z}. These three must be logically linked to each other (ie, same row, or column, or box). The fourth cell must have Z as one of its possible values, and it must line up with the {X, Z} and {Y, Z} cells by sharing a row, a column, or a 3x3 box with both.

When I'm stuck and I think the "XY-Wing" might help I concentrate on all the cells that have been reduced to pairs. I just review them one by one, looking to see if I can find neighboring cells that fit the pattern I've described. Sometimes I can find three cells that fit the "XYZ" pattern, but there is no fourth cell that lines up right to get any useful information. On a couple of puzzles I've located the "XY-Wing," but the value I was able to eliminate wasn't really useful for solving the rest of the puzzle.

I think practice is the only medicine for this one, Holly. dcb

PS BTW, you post on this forum quite a lot. When are you going to register?